basis

Subset of a vector space that allows defining coordinates

EntityQ189569

Also known as Hamel basis · algebraic basis · basis of a vector space · vector basis · base

Subclass of: subset
, basis

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, a set B of elements of a vector space V is called a basis if every element of V can be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called basis vectors.

Overview

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22 statements · 14% with external sources · numbers in brackets are citations

Different from: transcendence basis
basis element (topology)
base
basis
Has characteristic: linear independence
Facet of: linear algebra
Named after: Georg Hamel applies to name of subject: Hamel basis, 하멜 기저
Studied by: linear algebra
Opposite of: Schauder basis

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11 identifiers linking basis across the web's reference databases

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statements

14%

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Source last edited September 19, 2026. AIDB refreshes this page daily.

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AIDB. (2026). basis (Q189569). Retrieved from https://aidb.si/e/basis-Q189569